%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI660_1 : TPTP v8.1.2. Released v6.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 17:48:43 EDT 2023 % Result : Theorem 3.88s 1.45s % Output : Proof 4.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ARI660_1 : TPTP v8.1.2. Released v6.3.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n002.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 18:07:05 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.65 Running up to 7 provers in parallel. % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 1.85/1.08 Prover 0: Preprocessing ... % 1.85/1.08 Prover 2: Preprocessing ... % 1.85/1.08 Prover 3: Preprocessing ... % 1.85/1.08 Prover 5: Preprocessing ... % 1.85/1.08 Prover 6: Preprocessing ... % 1.85/1.08 Prover 1: Preprocessing ... % 1.85/1.08 Prover 4: Preprocessing ... % 2.22/1.15 Prover 4: Constructing countermodel ... % 2.22/1.15 Prover 6: Constructing countermodel ... % 2.22/1.15 Prover 5: Constructing countermodel ... % 2.22/1.15 Prover 1: Constructing countermodel ... % 2.22/1.15 Prover 0: Constructing countermodel ... % 2.22/1.15 Prover 2: Constructing countermodel ... % 2.22/1.15 Prover 3: Constructing countermodel ... % 3.88/1.44 Prover 5: proved (778ms) % 3.88/1.44 Prover 2: proved (779ms) % 3.88/1.44 Prover 3: proved (775ms) % 3.88/1.45 % 3.88/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.88/1.45 % 3.88/1.45 % 3.88/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.88/1.45 % 3.88/1.45 % 3.88/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.88/1.45 % 3.88/1.45 Prover 0: stopped % 3.88/1.45 Prover 6: stopped % 3.88/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.88/1.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.88/1.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.88/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.88/1.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.88/1.46 Prover 10: Preprocessing ... % 3.88/1.47 Prover 7: Preprocessing ... % 3.88/1.47 Prover 8: Preprocessing ... % 3.88/1.47 Prover 11: Preprocessing ... % 3.88/1.47 Prover 10: Constructing countermodel ... % 3.88/1.48 Prover 7: Constructing countermodel ... % 3.88/1.49 Prover 8: Constructing countermodel ... % 3.88/1.49 Prover 13: Preprocessing ... % 3.88/1.50 Prover 1: Found proof (size 31) % 3.88/1.50 Prover 11: Constructing countermodel ... % 3.88/1.50 Prover 1: proved (839ms) % 3.88/1.50 Prover 7: stopped % 4.47/1.50 Prover 8: stopped % 4.47/1.50 Prover 10: stopped % 4.47/1.50 Prover 11: stopped % 4.47/1.51 Prover 4: Found proof (size 31) % 4.47/1.51 Prover 4: proved (840ms) % 4.47/1.51 Prover 13: Constructing countermodel ... % 4.47/1.51 Prover 13: stopped % 4.47/1.51 % 4.47/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.47/1.51 % 4.47/1.52 % SZS output start Proof for theBenchmark % 4.47/1.52 Assumptions after simplification: % 4.47/1.52 --------------------------------- % 4.47/1.52 % 4.47/1.52 (conj) % 4.47/1.54 ? [v0: int] : ? [v1: int] : ($product(v0, a) = v1 & $product(a, a) = v0 & % 4.47/1.54 (($lesseq(v1, 10) & $lesseq(3, a)) | ($lesseq(11, v1) & $lesseq(a, 2)))) % 4.47/1.54 % 4.47/1.54 Those formulas are unsatisfiable: % 4.47/1.54 --------------------------------- % 4.47/1.54 % 4.47/1.54 Begin of proof % 4.47/1.54 | % 4.47/1.54 | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1 gives: % 4.47/1.55 | (1) $product(all_2_1, a) = all_2_0 & $product(a, a) = all_2_1 & % 4.47/1.55 | (($lesseq(all_2_0, 10) & $lesseq(3, a)) | ($lesseq(11, all_2_0) & % 4.47/1.55 | $lesseq(a, 2))) % 4.47/1.55 | % 4.47/1.55 | ALPHA: (1) implies: % 4.47/1.55 | (2) $product(a, a) = all_2_1 % 4.47/1.55 | (3) $product(all_2_1, a) = all_2_0 % 4.47/1.55 | (4) ($lesseq(all_2_0, 10) & $lesseq(3, a)) | ($lesseq(11, all_2_0) & % 4.47/1.55 | $lesseq(a, 2)) % 4.47/1.55 | % 4.47/1.55 | THEORY_AXIOM GroebnerMultiplication: % 4.47/1.55 | (5) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) | ~ ($product(v0, % 4.47/1.55 | v0) = v1)) % 4.47/1.55 | % 4.47/1.55 | GROUND_INST: instantiating (5) with a, all_2_1, simplifying with (2) gives: % 4.47/1.55 | (6) $lesseq(0, all_2_1) % 4.47/1.55 | % 4.47/1.55 | BETA: splitting (4) gives: % 4.47/1.55 | % 4.47/1.55 | Case 1: % 4.47/1.55 | | % 4.47/1.55 | | (7) $lesseq(all_2_0, 10) & $lesseq(3, a) % 4.47/1.55 | | % 4.47/1.55 | | ALPHA: (7) implies: % 4.47/1.55 | | (8) $lesseq(3, a) % 4.47/1.55 | | (9) $lesseq(all_2_0, 10) % 4.47/1.55 | | % 4.47/1.55 | | THEORY_AXIOM GroebnerMultiplication: % 4.47/1.56 | | (10) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 8)) | ~ ($lesseq(3, % 4.47/1.56 | | v0)) | ~ ($product(v0, v0) = v1)) % 4.47/1.56 | | % 4.47/1.56 | | GROUND_INST: instantiating (10) with a, all_2_1, simplifying with (2) gives: % 4.47/1.56 | | (11) ~ ($lesseq(all_2_1, 8)) | ~ ($lesseq(3, a)) % 4.47/1.56 | | % 4.47/1.56 | | BETA: splitting (11) gives: % 4.47/1.56 | | % 4.47/1.56 | | Case 1: % 4.47/1.56 | | | % 4.47/1.56 | | | (12) $lesseq(a, 2) % 4.47/1.56 | | | % 4.47/1.56 | | | COMBINE_INEQS: (8), (12) imply: % 4.47/1.56 | | | (13) $false % 4.47/1.56 | | | % 4.47/1.56 | | | CLOSE: (13) is inconsistent. % 4.47/1.56 | | | % 4.47/1.56 | | Case 2: % 4.47/1.56 | | | % 4.47/1.56 | | | (14) $lesseq(9, all_2_1) % 4.47/1.56 | | | % 4.47/1.56 | | | THEORY_AXIOM GroebnerMultiplication: % 4.47/1.56 | | | (15) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, % 4.47/1.56 | | | $difference($product(3, v1), v2))) | ~ ($lesseq(0, v1)) | % 4.47/1.56 | | | ~ ($lesseq(3, v0)) | ~ ($product(v1, v0) = v2)) % 4.47/1.56 | | | % 4.47/1.56 | | | GROUND_INST: instantiating (15) with a, all_2_1, all_2_0, simplifying with % 4.47/1.56 | | | (3) gives: % 4.47/1.56 | | | (16) ~ ($lesseq(1, $difference($product(3, all_2_1), all_2_0))) | ~ % 4.47/1.56 | | | ($lesseq(0, all_2_1)) | ~ ($lesseq(3, a)) % 4.47/1.56 | | | % 4.47/1.56 | | | BETA: splitting (16) gives: % 4.47/1.56 | | | % 4.47/1.56 | | | Case 1: % 4.47/1.56 | | | | % 4.47/1.56 | | | | (17) $lesseq(all_2_1, -1) % 4.47/1.56 | | | | % 4.47/1.56 | | | | COMBINE_INEQS: (6), (17) imply: % 4.47/1.56 | | | | (18) $false % 4.47/1.56 | | | | % 4.47/1.57 | | | | CLOSE: (18) is inconsistent. % 4.47/1.57 | | | | % 4.47/1.57 | | | Case 2: % 4.47/1.57 | | | | % 4.47/1.57 | | | | (19) ~ ($lesseq(1, $difference($product(3, all_2_1), all_2_0))) | ~ % 4.47/1.57 | | | | ($lesseq(3, a)) % 4.47/1.57 | | | | % 4.47/1.57 | | | | BETA: splitting (19) gives: % 4.47/1.57 | | | | % 4.47/1.57 | | | | Case 1: % 4.47/1.57 | | | | | % 4.47/1.57 | | | | | (20) $lesseq(a, 2) % 4.47/1.57 | | | | | % 4.47/1.57 | | | | | COMBINE_INEQS: (8), (20) imply: % 4.47/1.57 | | | | | (21) $false % 4.47/1.57 | | | | | % 4.47/1.57 | | | | | CLOSE: (21) is inconsistent. % 4.47/1.57 | | | | | % 4.47/1.57 | | | | Case 2: % 4.47/1.57 | | | | | % 4.47/1.57 | | | | | (22) $lesseq(0, $difference(all_2_0, $product(3, all_2_1))) % 4.47/1.57 | | | | | % 4.47/1.57 | | | | | COMBINE_INEQS: (9), (22) imply: % 4.47/1.57 | | | | | (23) $lesseq(all_2_1, 3) % 4.47/1.57 | | | | | % 4.47/1.57 | | | | | SIMP: (23) implies: % 4.47/1.57 | | | | | (24) $lesseq(all_2_1, 3) % 4.47/1.57 | | | | | % 4.47/1.57 | | | | | COMBINE_INEQS: (14), (24) imply: % 4.47/1.57 | | | | | (25) $false % 4.47/1.57 | | | | | % 4.47/1.57 | | | | | CLOSE: (25) is inconsistent. % 4.47/1.57 | | | | | % 4.47/1.57 | | | | End of split % 4.47/1.57 | | | | % 4.47/1.57 | | | End of split % 4.47/1.57 | | | % 4.47/1.57 | | End of split % 4.47/1.57 | | % 4.47/1.57 | Case 2: % 4.47/1.57 | | % 4.47/1.57 | | (26) $lesseq(11, all_2_0) & $lesseq(a, 2) % 4.47/1.57 | | % 4.47/1.57 | | ALPHA: (26) implies: % 4.47/1.57 | | (27) $lesseq(a, 2) % 4.47/1.57 | | (28) $lesseq(11, all_2_0) % 4.47/1.57 | | % 4.47/1.57 | | THEORY_AXIOM GroebnerMultiplication: % 4.47/1.57 | | (29) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(9, v2)) | % 4.47/1.57 | | ~ ($lesseq(v0, 2)) | ~ ($product(v1, v0) = v2) | ~ ($product(v0, % 4.47/1.57 | | v0) = v1)) % 4.47/1.57 | | % 4.47/1.57 | | GROUND_INST: instantiating (29) with a, all_2_1, all_2_0, simplifying with % 4.47/1.57 | | (2), (3) gives: % 4.47/1.57 | | (30) ~ ($lesseq(9, all_2_0)) | ~ ($lesseq(a, 2)) % 4.47/1.57 | | % 4.47/1.57 | | BETA: splitting (30) gives: % 4.47/1.57 | | % 4.47/1.57 | | Case 1: % 4.47/1.57 | | | % 4.47/1.57 | | | (31) $lesseq(3, a) % 4.47/1.57 | | | % 4.47/1.57 | | | COMBINE_INEQS: (27), (31) imply: % 4.47/1.58 | | | (32) $false % 4.47/1.58 | | | % 4.47/1.58 | | | CLOSE: (32) is inconsistent. % 4.47/1.58 | | | % 4.47/1.58 | | Case 2: % 4.47/1.58 | | | % 4.47/1.58 | | | (33) $lesseq(all_2_0, 8) % 4.47/1.58 | | | % 4.47/1.58 | | | COMBINE_INEQS: (28), (33) imply: % 4.47/1.58 | | | (34) $false % 4.47/1.58 | | | % 4.47/1.58 | | | CLOSE: (34) is inconsistent. % 4.47/1.58 | | | % 4.47/1.58 | | End of split % 4.47/1.58 | | % 4.47/1.58 | End of split % 4.47/1.58 | % 4.47/1.58 End of proof % 4.47/1.58 % SZS output end Proof for theBenchmark % 4.47/1.58 % 4.47/1.58 943ms %------------------------------------------------------------------------------